class Solution {
public:
    int minFallingPathSum(vector<vector<int>>& matrix) {
        int n = matrix.size();

        vector<vector<int>> dp(n + 1, vector<int> (n + 2, INT_MAX)); 

        for(int i = 0; i <= n + 1; ++i)
            dp[0][i] = 0;

        int ret = INT_MAX;
        for(int i = 1; i <= n; ++i)
        {
            for(int j = 1; j <= n; ++j)
            {
                dp[i][j] = min({dp[i - 1][j - 1], dp[i - 1][j], dp[i - 1][j + 1]}) 
                    + matrix[i - 1][j - 1];
                if(i == n) ret = min(ret, dp[i][j]);
            }
        }
        return ret;
    }
};
